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The observation of the as-grown crystal surface is an important way of investigating the epitaxial growth mechanism. There are a number of studies on the two-dimensional crystal growth by examining the stacking faults, growth spirals and stacking fault shadows on the as-grown silicon and germanium crystal surfaces. Although a perfect crystal is essential for the manufacture of electronic devices, crystal growth would not proceed without imperfections. Screw dislocations are regarded as constituting the growth nucleus. While the screw structure accompanied by stacking faults is frequently found, the growth nucleus generated by simple screw dislocations is seldom observed. In previous work, we have reported that perfect crystal growth can be achieved by forming defect-free pyramidal hillocks using the temperature pulsing method. Spiral growth layers, stacking faults and the stacking fault shadows on the as-grown III–V compound semiconductor surfaces grown by vapor- and liquid-phase epitaxy have been already reported. This paper presents our recent study of spiral growth layers and the circular growth nucleus.

We determine the pressure distribution behind a soft contact lens that is necessary to keep the lens in conformity with an axisymmetric substrate. The substrate consists of two regions: a central portion, the cornea, supposed to be an ellipsoid; and a peripheral region, the sclera, taken to be a sphere. The pressure is obtained as part of a numerical solution of the axisymmetric equilibrium equations for an initially curved, linearly elastic membrane. The relaxed shape of the lens is assumed to be an axisymmetric ellipsoid with a central curvature and a shape factor different from those of the cornea. The variation in the thickness of the lens from its center to edge is approximated by a polynomial. Pressure distributions are obtained for several typical soft contact lens fittings.

Some binary operations of fuzzy numbers are reviewed and a limit of a sequence of fuzzy numbers is defined. Based on these concepts and properties, finite and countable fuzzy random variables are considered and a convergence property of a sequence of fuzzy random variables is shown.